Maximum likelihood estimation and inference for high dimensional generalized factor models with application to factor-augmented regressions

• Published in: Journal of econometrics Vol. 229; no. 1; pp. 180 - 200
• Main Author: Wang, Fa
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2022; Elsevier Sequoia S.A
• Subjects: Asymptotic methods; Augmentation; Convergence; Density; econometrics; Estimating techniques; estimation; Factor model; Factor-augmented regression; Forecasting; High dimension; mass; Maximum likelihood; Maximum likelihood method; Mixed measurement; Nonlinear analysis; nonlinear models; Nonlinear systems; Normality; Probability; probability distribution; statistical models; High dimension; Factor model; C13; C35; Factor-augmented regression; Mixed measurement; Maximum likelihood; Forecasting
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2020.11.002

This paper reestablishes the main results in Bai (2003) and Bai and Ng (2006) for generalized factor models, with slightly stronger conditions on the relative magnitude of N (number of subjects) and T (number of time periods). Convergence rates of the estimated factor space and loading space and asymptotic normality of the estimated factors and loadings are established under mild conditions that allow for linear, Logit, Probit, Tobit, Poisson and some other single-index nonlinear models. The probability density/mass function is allowed to vary across subjects and time, thus mixed models are also allowed for. For factor-augmented regressions, this paper establishes the limit distributions of the parameter estimates, the conditional mean, and the forecast when factors estimated from nonlinear/mixed data are used as proxies for the true factors.